You can move any amount of data over Serial. You can even program an Arduino over Serial! (that's the regular way even). No restriction there.
Serial needs three wires. Two data, TX and RX, plus GND. For your phone Arduino you'd need a fourth wire: power. That's it, the other two wires you have are spares in this case.
You could produce different voltages for your keys - 18 levels in all - and do an analogRead on them. Probably much easier to wire them in a matrix and have an Arduino read them (a Pro Mini will fit easily). That same Arduino will then drive your LCD display, displaying temperature or whatever you want on the LCD.
The "master" Arduino could be hidden somewhere in the dash or the centre console, and that one would read the sensors and drive the lights. Then either on request, or on schedule, it would send the data to the handset Arduino. The moment a button is pressed, the handset would send a command (could be as little as a single character) to the master telling it which lights to switch on/off etc.